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Our interest in this thesis is first to combine the different measurement techniques for operational risk in financial companies, and we highlight more and more the consequences of estimation risk which is treated as a particular part of operational risk. In the first part, we will present a full overview of operational risk, from the regulatory laws and regulations to the associated mathematical and actuarial concepts as well as a numerical application regarding the Advanced Measurement Approach, like Loss Distribution to calculate the capital requirement, then applying the Extreme Value Theory. We conclude this first part by setting a scaling technique based on (OLS) enabling us to normalize our external data to a local Lebanese Bank. On the second part, we feature estimation risk by first measuring the error induced on the SCR by the estimation error of the parameters, to having an alternative yield curve estimation and finishing by calling attention to the reflections on assumptions of the calculation instead of focusing on the so called hypothesis "consistent with market values", would be more appropriate and effective than to complicate models and generate additional errors and instability. Chapters in this part illustrate the estimation risk in its different aspects which is a part of operational risk, highlighting as so the attention that should be given in treating our models

距離期望值4至6倍標準差以外的罕見機率電流值，是當前積體電路設計品質的關鍵之一，但隨著精確度的標準提升，實務上以蒙地卡羅方法模擬電路資料，因曠日廢時愈發不可行，而過去透過參數模型外插估計或迴歸分析方法，也因變數蒐集不易、操作電壓減小使得電流值尾端估計產生偏差，上述原因使得尾端電流值估計困難。因此本文引進統計方法改善罕見機率電流值的估計：先以Box-Cox轉換觀察值為近似常態，改善尾端分配值的估計，再以加權迴歸方法估計罕見電流值，其中迴歸解釋變數為Log或Z分數轉換的經驗累積機率，而加權方法採用Down-weight加重極值樣本資訊的重要性，此外，本研究也考慮能蒐集完整變數的情況，改以電路資料作為解釋變數進行加權迴歸。另一方面，本研究也採用極值理論作為估計方法。 本文先以電腦模擬評估各方法的優劣，假設母體分配為常態、T分配、Gamma分配，以均方誤差作為衡量指標，模擬結果驗證了加權迴歸方法的可行性。而後參考模擬結果決定篩選樣本方式進行實證研究，資料來源為新竹某科技公司，實證結果顯示加權迴歸配合Box-Cox轉換能以十萬筆樣本數，準確估計左、右尾機率10^(-4) 、10^(-5)、10^(-6)、10^(-7)極端電流值。其中右尾部分的加權迴歸解釋變數採用對數轉換，而左尾部分的加權迴歸解釋變數採用Z分數轉換，估計結果較為準確，又若能蒐集電路資訊作為解釋變數，在左尾部份可以有最準確的估計結果；而篩選樣本尾端1%和整筆資料的方式對於不同方法的估計準確度各有利弊，皆可考慮。另外，1%門檻值比例的極值理論能穩定且中等程度的估計不同電壓下的電流值，且有短程估計最準的趨勢。 / To obtain the tail distribution of current beyond 4 to 6 sigma is nowadays a key issue in integrated circuit (IC) design and computer simulation is a popular tool to estimate the tail values. Since creating rare events via simulation is time-consuming, often the linear extrapolation methods (such as regression analysis) are applied to enhance efficiency. However, it is shown from past work that the tail values is likely to behave differently if the operating voltage is getting lower. In this study, a statistical method is introduced to deal with the lower voltage case. The data are evaluated via the Box-Cox (or power) transformation and see if they need to be transformed into normally distributed data, following by weighted regression to extrapolate the tail values. In specific, the independent variable is the empirical CDF with logarithm or z-score transformation, and the weight is down-weight in order to emphasize the information of extreme values observations. In addition to regression analysis, Extreme Value Theory (EVT) is also adopted in the research. The computer simulation and data sets from a famous IC manufacturer in Hsinchu are used to evaluate the proposed method, with respect to mean squared error. In computer simulation, the data are assumed to be generated from normal, student t, or Gamma distribution. For empirical data, there are 10^8 observations and tail values with probabilities 10^(-4),10^(-5),10^(-6),10^(-7) are set to be the study goal given that only 10^5 observations are available. Comparing to the traditional methods and EVT, the proposed method has the best performance in estimating the tail probabilities. If the IC current is produced from regression equation and the information of independent variables can be provided, using the weighted regression can reach the best estimation for the left-tailed rare events. Also, using EVT can also produce accurate estimates provided that the tail probabilities to be estimated and the observations available are on the similar scale, e.g., probabilities 10^(-5)~10^(-7) vs.10^5 observations.

Submitted by Eduardo Alonso Marza dos Santos (eduardo.marza.santos@gmail.com) on 2015-06-21T10:30:55Z No. of bitstreams: 1 Eduardo_A_M_Santos.pdf: 646820 bytes, checksum: aaba122a576d7c75ad0e5803539c25d4 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2015-06-22T11:46:18Z (GMT) No. of bitstreams: 1 Eduardo_A_M_Santos.pdf: 646820 bytes, checksum: aaba122a576d7c75ad0e5803539c25d4 (MD5) / Made available in DSpace on 2015-06-22T11:56:18Z (GMT). No. of bitstreams: 1 Eduardo_A_M_Santos.pdf: 646820 bytes, checksum: aaba122a576d7c75ad0e5803539c25d4 (MD5) Previous issue date: 2015-05-28 / The dissertation goal is to quantify the tail risk premium embedded into hedge funds' returns. Tail risk is the probability of extreme large losses. Although it is a rare event, asset pricing theory suggests that investors demand compensation for holding assets sensitive to extreme market downturns. By de nition, such events have a small likelihood to be represented in the sample, what poses a challenge to estimate the e ects of tail risk by means of traditional approaches such as VaR. The results show that it is not su cient to account for the tail risk stemming from equities markets. Active portfolio management employed by hedge funds demand a speci c measure to estimate and control tail risk. Our proposed factor lls that void inasmuch it presents explanatory power both over the time series as well as the cross-section of funds' returns. / O objetivo do trabalho é quanti car o prêmio de risco de cauda presente nos retornos de fundos de investimento americanos. Risco de cauda é o risco de perdas excepcionalmente elevadas. Apesar de ser um evento raro, a teoria de apreçamento de ativos sugere que os investidores exigem um prêmio de risco para reter ativos expostos a eventos negativos extremos (eventos de cauda). Por de nição, observações extremas têm baixa probabilidade de estarem presentes na amostra, o que di culta a estimação dos impactos de risco de cauda sobre os retornos e reduz o poder de técnicas tradicionais como VaR. Os resultados indicam que não é su ciente controlar somente para o risco de cauda do mercado de capitais. A gestão ativa de portfólio por parte dos gestores de fundos requer uma medida própria para estimação e o controle de risco de cauda. O fator de risco de cauda que propomos cumpre este papel ao apresentar poder explicativo tanto na série temporal dos retornos quanto no corte transversal.

Submitted by Edimilson Costa Lucas (costalucas@yahoo.com) on 2015-11-10T13:28:51Z No. of bitstreams: 1 EdimilsonCostaLucas_TESE.pdf: 2525096 bytes, checksum: 88b5fc4a39e14115350d9a7fddece121 (MD5) / Approved for entry into archive by Maria Tereza Fernandes Conselmo (maria.conselmo@fgv.br) on 2015-11-11T12:34:10Z (GMT) No. of bitstreams: 1 EdimilsonCostaLucas_TESE.pdf: 2525096 bytes, checksum: 88b5fc4a39e14115350d9a7fddece121 (MD5) / Made available in DSpace on 2015-11-11T12:38:48Z (GMT). No. of bitstreams: 1 EdimilsonCostaLucas_TESE.pdf: 2525096 bytes, checksum: 88b5fc4a39e14115350d9a7fddece121 (MD5) Previous issue date: 2015-10-19 / The occurrence of extreme weather events, such as increased temperature, hurricanes, floods and droughts has been increasingly common around of the world. The finance literature has documented efforts directed to the assessment of economic impacts from climate change that can bring significant consequences for the world economy. However, especially in Brazil, a key emerging market, little has been studied mainly with a view to assessing the impacts of climate events in the company level. Thus, this thesis analyzes, in an unprecedented manner, the impact of weather events on the value of companies belonging to two high national interest industries, in the form of two essays. First it analyzes the impact of extreme rainfall on the stock price of the Brazilian food sector. Therefore, it is conducted the research using daily data in share prices of six companies of this industry. From the location to the main area of activity of these companies, they are considered their daily data on extreme rainfall. With the use of hybrid methodology ARMA-GARCH-GPD, it was found that the evaluated companies, the extreme rainfall impacted significantly in more than half of the 198 days of extreme rainfall between 02/28/2005 and 12/30/2014, resulting in average losses daily around 1.97% on the day after the heavy rainfall. In terms of market value, this represents total average loss of around US$ 682.15 million in a single day. Second it evaluates the impact of climate variables and location on the value of companies in the energy sector in Brazil, from data on companies in the Brazilian electricity sector, as well as rainfall, temperature and geographical location of the companies. From the analysis of data in static panel and spatial panel, the results suggest that temperature and precipitation have significant effect on the value of these companies. This study can contribute in the process of structuring and creating a weather derivatives market in Brazil. / A ocorrência de eventos climáticos extremos, tais como aumento da temperatura, furacões, enchentes e secas, tem sido cada vez mais frequente ao redor do mundo. A literatura de finanças tem documentado esforços dirigidos à avaliação de impactos econômicos oriundos das variações climáticas, com consequências significantes na economia mundial. Entretanto, especialmente no Brasil, um dos principais mercados emergentes, pouco tem sido pesquisado, sobretudo com vistas à avaliação dos impactos de eventos climáticos no nível das empresas. Sendo assim, esta tese analisa, de forma inédita, o impacto de eventos climáticos sobre o valor de empresas pertencentes a duas indústrias de elevado interesse nacional, sob a forma de dois ensaios. Em primeiro lugar analisa-se o impacto de chuvas extremas sobre o preço de ações do setor de alimentos brasileiro. Para tanto, é conduzida a pesquisa empregando dados diários do preço de ações de seis empresas dessa indústria. A partir da localização da principal região de atuação dessas empresas, são considerados os respectivos dados diários referentes às chuvas extremas. Com o emprego da metodologia híbrida ARMA-GARCH-GPD, constatou-se que, nas empresas avaliadas, as chuvas extremas impactaram significantemente em mais da metade dos 198 dias de chuvas extremas ocorridos entre 28/02/2005 e 30/12/2014, acarretando perdas médias diárias ao redor de 1,97% no dia posterior a chuva extrema. Em termos de valor de mercado, isso representa perda média total ao redor de US$682,15 mi em um único dia. Em segundo lugar avalia-se o impacto de variáveis climáticas e localização sobre o valor das empresas do setor de energia do Brasil, a partir de dados referentes às empresas do setor elétrico brasileiro, bem como precipitação pluviométrica, temperatura e localização geográfica das empresas. A partir da análise de dados em painel estático e painel espacial, os resultados sugerem que temperatura e precipitação pluviométrica têm efeito significante sobre o valor dessas empresas. O presente estudo pode vir a contribuir no processo de estruturação e criação de um mercado de derivativos climáticos no Brasil.

Made available in DSpace on 2010-04-20T21:00:30Z (GMT). No. of bitstreams: 3 marciocecilioturma2004.pdf.jpg: 19602 bytes, checksum: 0772484d1cb46349dfbfb25620b5cdae (MD5) marciocecilioturma2004.pdf: 859203 bytes, checksum: 346a3e7d5751118ff894a182d7512b56 (MD5) marciocecilioturma2004.pdf.txt: 86793 bytes, checksum: e0c91b2715fc569bc6ec29bfce078e69 (MD5) Previous issue date: 2007-01-23T00:00:00Z / Há forte evidência que os retornos das séries financeiras apresentam caudas mais pesadas que as da distribuição normal, principalmente em mercados emergentes. No entanto, muitos modelos de risco utilizados pelas instituições financeiras baseiam-se em normalidade condicional ou não condicional, reduzindo a acurácia das estimativas. Os recentes avanços na Teoria de Valores Extremos permitem sua aplicação na modelagem de risco, como por exemplo, na estimação do Valor em Risco e do requerimento de capital. Este trabalho verifica a adequação de um procedimento proposto por McNeil e Frey [1999] para estimação do Valor em Risco e conseqüente requerimento de capital às principais séries financeiras de retornos do Brasil. Tal procedimento semi-paramétrico combina um modelo GARCH ajustado por pseudo máxima verossimilhança para estimação da volatilidade corrente com a Teoria de Valores Extremos para estimação das caudas da distribuição das inovações do modelo GARCH. O procedimento foi comparado através de backtestings com outros métodos mais comuns de estimação de VaR que desconsideram caudas pesadas das inovações ou a natureza estocástica da volatilidade. Concluiu-se que o procedimento proposto por McNeil e Frey [1999] mostrou melhores resultados, principalmente para eventos relacionados a movimentos negativos nos mercados . Futuros trabalhos consistirão no estudo de uma abordagem multivariada de grandes dimensões para estimação de VaR e requerimento de capital para carteiras de investimentos. / There is a strong evidence that financial return series are heavy-tailed, mostly in emerging markets. However, most of the risk models used by financial institutions are based in conditional or non-conditional normality, which reduces the accuracy of the estimates. The recent advances in Extreme Value Theory permit its application to risk measuring, such as Value at Risk and capital adequacy estimates. This work verifies the adequacy of a procedure proposed by McNeil and Frey [1999] to VaR and consequent capital requirement estimates for the main financial return series in Brazil. This semi parametric procedure combines a pseudo-maximumlikelihood fitting GARCH model to estimate the current volatility and the Extreme Value Theory (EVT) to estimate the tails of the innovations distribution of the GARCH model. Using backtestings the procedure was compared to other common methods of VaR estimation that disregard heavy tails of the innovations or the stochastic nature of the volatility. The procedure proposed by McNeil and Frey [1999] showed better results, mostly for negative events in the financial market2 . Further works will consist of studying a high dimensional multivariate approach to estimate VaR and capital requirements for portfolios of investment instruments.

Cette thèse s'inscrit dans le contexte de la statistique des valeurs extrêmes. Elle y apporte deux contributions principales. Dans la littérature récente en statistique des valeurs extrêmes, un modèle de queues de distributions a été introduit afin d'englober aussi bien les lois de type Pareto que les lois à queue de type Weibull. Les deux principaux types de décroissance de la fonction de survie sont ainsi modélisés. Un estimateur des quantiles extrêmes a été déduit de ce modèle mais il dépend de deux paramètres inconnus, le rendant inutile dans des situations pratiques. La première contribution de cette thèse est de proposer des estimateurs de ces paramètres. Insérer nos estimateurs dans l'estimateur des quantiles extrêmes précédent permet alors d'estimer des quantiles extrêmes pour des lois de type Pareto aussi bien que pour des lois à queue de type Weibull d'une façon unifiée. Les lois asymptotiques de nos trois nouveaux estimateurs sont établies et leur efficacité est illustrée sur des données simulées et sur un jeu de données réelles de débits de la rivière Nidd se situant dans le Yorkshire en Angleterre. La seconde contribution de cette thèse consiste à introduire et estimer une nouvelle mesure de risque appelé Conditional Tail Moment. Elle est définie comme le moment d'ordre a>0 de la loi des pertes au-delà du quantile d'ordre p appartenant à ]0,1[ de la fonction de survie. Estimer le Conditional Tail Moment permet d'estimer toutes les mesures de risque basées sur les moments conditionnels telles que la Value-at-Risk, la Conditional Tail Expectation, la Conditional Value-at-Risk, la Conditional Tail Variance ou la Conditional Tail Skewness. Ici, on s'intéresse à l'estimation de ces mesures de risque dans le cas de pertes extrêmes c'est-à-dire lorsque p tend vers 0 lorsque la taille de l'échantillon augmente. On suppose également que la loi des pertes est à queue lourde et qu'elle dépend d'une covariable. Les estimateurs proposés combinent des méthodes d'estimation non-paramétrique à noyau avec des méthodes issues de la statistique des valeurs extrêmes. Le comportement asymptotique de nos estimateurs est établi et illustré aussi bien sur des données simulées que sur des données réelles de pluviométrie provenant de la région Cévennes-Vivarais. / This thesis can be viewed within the context of extreme value statistics. It provides two main contributions to this subject area. In the recent literature on extreme value statistics, a model on tail distributions which encompasses Pareto-type distributions as well as Weibull tail-distributions has been introduced. The two main types of decreasing of the survival function are thus modeled. An estimator of extreme quantiles has been deduced from this model, but it depends on two unknown parameters, making it useless in practical situations. The first contribution of this thesis is to propose estimators of these parameters. Plugging our estimators in the previous extreme quantiles estimator allows us to estimate extreme quantiles from Pareto-type and Weibull tail-distributions in an unified way. The asymptotic distributions of our three new estimators are established and their efficiency is illustrated on a simulation study and on a real data set of exceedances of the Nidd river in the Yorkshire (England). The second contribution of this thesis is the introduction and the estimation of a new risk measure, the so-called Conditional Tail Moment. It is defined as the moment of order a>0 of the loss distribution above the quantile of order p in (0,1) of the survival function. Estimating the Conditional Tail Moment permits to estimate all risk measures based on conditional moments such as the Value-at-Risk, the Conditional Tail Expectation, the Conditional Value-at-Risk, the Conditional Tail Variance or the Conditional Tail Skewness. Here, we focus on the estimation of these risk measures in case of extreme losses i.e. when p converges to 0 when the size of the sample increases. It is moreover assumed that the loss distribution is heavy-tailed and depends on a covariate. The estimation method thus combines nonparametric kernel methods with extreme-value statistics. The asymptotic distribution of the estimators is established and their finite sample behavior is illustrated both on simulated data and on a real data set of daily rainfalls in the Cévennes-Vivarais region (France).

The study of randomly excited nonlinear dynamical systems forms the focus of this thesis. We discuss two classes of problems: first, the characterization of nonlinear random response of the system before it comes into existence and, the second, assimilation of measured responses into the mathematical model of the system after the system comes into existence. The first class of problems constitutes forward problems while the latter belongs to the class of inverse problems. An outstanding feature of these problems is that they are almost always not amenable for exact solutions. We tackle in the present study these two classes of problems using Monte Carlo simulation tools in conjunction with Markov process theory, Bayesian model updating strategies, and particle filtering based dynamic state estimation methods. It is well recognized in literature that any successful application of Monte Carlo simulation methods to practical problems requires the simulation methods to be reinforced with effective means of controlling sampling variance. This can be achieved by incorporating any problem specific qualitative and (or) quantitative information that one might have about system behavior in formulating estimators for response quantities of interest. In the present thesis we outline two such approaches for variance reduction. The first of these approaches employs a substructuring scheme, which partitions the system states into two sets such that the probability distribution of the states in one of the sets conditioned on the other set become amenable for exact analytical solution. In the second approach, results from data based asymptotic extreme value analysis are employed to tackle problems of time variant reliability analysis and updating of this reliability. We exemplify in this thesis the proposed approaches for response estimation and model updating by considering wide ranging problems of interest in structural engineering, namely, nonlinear response and reliability analyses under stationary and (or) nonstationary random excitations, response sensitivity model updating, force identification, residual displacement analysis in instrumented inelastic structures under transient excitations, problems of dynamic state estimation in systems with local nonlinearities, and time variant reliability analysis and reliability model updating. We have organized the thesis into eight chapters and three appendices. A resume of contents of these chapters and appendices follows. In the first chapter we aim to provide an overview of mathematical tools which form the basis for investigations reported in the thesis. The starting point of the study is taken to be a set of coupled stochastic differential equations, which are obtained after discretizing spatial variables, typically, based on application of finite element methods. Accordingly, we provide a summary of the following topics: (a) Markov vector approach for characterizing time evolution of transition probability density functions, which includes the forward and backward Kolmogorov equations, (b) the equations governing the time evolution of response moments and first passage times, (c) numerical discretization of governing stochastic differential equation using Ito-Taylor’s expansion, (d) the partial differential equation governing the time evolution of transition probability density functions conditioned on measurements for the study of existing instrumented structures, (e) the time evolution of response moments conditioned on measurements based on governing equations in (d), and (f) functional recursions for evolution of multidimensional posterior probability density function and posterior filtering density function, when the time variable is also discretized. The objective of the description here is to provide an outline of the theoretical formulations within which the problems of response estimation and model updating are formulated in the subsequent chapters of the present thesis. We briefly state the class of problems, which are amenable for exact solutions. We also list in this chapter major text books, research monographs, and review papers relevant to the topics of nonlinear random vibration analysis and dynamic state estimation. In Chapter 2 we provide a review of literature on solutions of problems of response analysis and model updating in nonlinear dynamical systems. The main focus of the review is on Monte Carlo simulation based methods for tackling these problems. The review accordingly covers numerical methods for approximate solutions of Kolmogorov equations and associated moment equations, variance reduction in simulation based analysis of Markovian systems, dynamic state estimation methods based on Kalman filter and its variants, particle filtering, and variance reduction based on Rao-Blackwellization. In this review we chiefly cover papers that have contributed to the growth of the methodology. We also cover briefly, the efforts made in applying the ideas to structural engineering problems. Based on this review, we identify the problems of variance reduction using substructuring schemes and data based extreme value analysis and, their incorporation into response estimation and model updating strategies, as problems requiring further research attention. We also identify a range of problems where these tools could be applied. We consider the development of a sequential Monte Carlo scheme, which incorporates a substructuring strategy, for the analysis of nonlinear dynamical systems under random excitations in Chapter 3. The proposed substructuring ensures that a part of the system states conditioned on the remaining states becomes Gaussian distributed and is amenable for an exact analytical solution. The use of Monte Carlo simulations is subsequently limited for the analysis of the remaining system states. This clearly results in reduction in sampling variance since a part of the problem is tackled analytically in an exact manner. The successful performance of the proposed approach is illustrated by considering response analysis of a single degree of freedom nonlinear oscillator under random excitations. Arguments based on variance decomposition result and Rao-Blackwell theorems are presented to demonstrate that the proposed variance reduction indeed is effective. In Chapter 4, we modify the sequential Monte Carlo simulation strategy outlined in the preceding chapter to incorporate questions of dynamic state estimation when data on measured responses become available. Here too, the system states are partitioned into two groups such that the states in one group become Gaussian distributed when conditioned on the states in the other group. The conditioned Gaussian states are subsequently analyzed exactly using the Kalman filter and, this is interfaced with the analysis of the remaining states using sequential importance sampling based filtering strategy. The development of this combined Kalman and sequential importance sampling filtering method constitutes one of the novel elements of this study. The proposed strategy is validated by considering the problem of dynamic state estimation in linear single and multi-degree of freedom systems for which exact analytical solutions exist. In Chapter 5, we consider the application of the tools developed in Chapter 4 for a class of wide ranging problems in nonlinear random vibrations of existing systems. The nonlinear systems considered include single and multi-degree of freedom systems, systems with memoryless and hereditary nonlinearities, and stationary and nonstationary random excitations. The specific applications considered include nonlinear dynamic state estimation in systems with local nonlinearities, estimation of residual displacement in instrumented inelastic dynamical system under transient random excitations, response sensitivity model updating, and identification of transient seismic base motions based on measured responses in inelastic systems. Comparisons of solutions from the proposed substructuring scheme with corresponding results from direct application of particle filtering are made and a satisfactory mutual agreement is demonstrated. We consider next questions on time variant reliability analysis and corresponding model updating in Chapters 6 and 7, respectively. The research effort in these studies is focused on exploring the application of data based asymptotic extreme value analysis for problems on hand. Accordingly, we investigate reliability of nonlinear vibrating systems under stochastic excitations in Chapter 6 using a two-stage Monte Carlo simulation strategy. For systems with white noise excitation, the governing equations of motion are interpreted as a set of Ito stochastic differential equations. It is assumed that the probability distribution of the maximum over a specified time duration in the steady state response belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of selection of the form of the extreme value distribution based on hypothesis testing, and, the next stage involves the estimation of parameters of the relevant extreme value distribution. Both these stages are implemented using data from limited Monte Carlo simulations of the system response. The proposed procedure is illustrated with examples of linear/nonlinear systems with single/multiple degrees of freedom driven by random excitations. The predictions from the proposed method are compared with the results from large scale Monte Carlo simulations, and also with the classical analytical results, when available, from the theory of out-crossing statistics. Applications of the proposed method for vibration data obtained from laboratory conditions are also discussed. In Chapter 7 we consider the problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations. Here we assume that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes’ theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplified by considering the reliability analysis of a few low dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on limited amount of pertinent Monte Carlo simulations. A summary of the contributions made and a few suggestions for future work are presented in Chapter 8. The thesis also contains three appendices. Appendix A provides details of the order 1.5 strong Taylor scheme that is extensively employed at several places in the thesis. The formulary pertaining to the bootstrap and sequential importance sampling particle filters is provided in Appendix B. Some of the results on characterizing conditional probability density functions that have been used in the development of the combined Kalman and sequential importance sampling filter in Chapter 4 are elaborated in Appendix C.

Nous appliquons la théorie asymptotique des expériences statistiques à des problèmes liés aux valeurs extrêmes. Quatre modèles semi-paramétriques sont envisagés. Tout d'abord le modèle d'échantillonnage de fonction de répartition de type Pareto. L'index de Pareto est le paramètre d'intérêt tandis que la fonction à variation lente, qui intervient dans la décomposition de la fonction de survie, joue le rôle de nuisance. Nous considérons ensuite des observations i.i.d. de fonction de répartition de type Weibull. Le troisième modèle étudié est un modèle de régression. On considère des couples d'observations $(Y_i,X_i)$ indépendants, les v.a. $X_i$ sont i.i.d. de loi connue et on suppose que la fonction de répartition de la loi de $Y$ conditionnellement à $X$ est de type Pareto, avec une fonction à variation lente et un index $gamma$ qui dépendent de $X$. On fait l'hypothèse que la fonction $gamma$ a une forme quelconque mais connue, qui dépend d'un paramètre $\ / Doctorat en sciences, Orientation statistique / info:eu-repo/semantics/nonPublished

Dans cette thèse, nous étudions la garantie tempête consacrée aux dommages causés par le vent et un développement de l'assurance comportementale à travers le risque automobile. Nous associons des informations extérieures comme la vitesse du vent aux données de l'assurance. Nous proposons la construction d'un indice tempête pour compléter et renforcer l'évaluation des dégâts causés par les tempêtes majeures. Nous définissons ensuite un partage du territoire français en 6 zones tempêtes, dépendant des corrélations extrêmes de vent, pour tester plusieurs scénarios. Ces différents tests et considérations nous permettent d'améliorer notre indice tempête. Nous nous appuyons sur les modèles de la théorie des valeurs extrêmes pour montrer l'impact de la variabilité sur le calcul des périodes de retour et besoins en fonds propres. Nous soulignons ainsi les difficultés rencontrées pour dégager des résultats robustes en lien avec les évènements extrêmes. Pour ce qui est de l'assurance automobile, nous testons différentes méthodes pour répondre aux évolutions techniques et réglementaires. Nous caractérisons la partition homme / femme en utilisant la procédure logistique, l'analyse des correspondances multiples ou les arbres de classification. Nous montrons qu'il est possible de compenser l'absence de la variable sexe par d'autres informations spécifiques à l'assuré ou à son véhicule et en particulier l'utilisation de relevés kilométriques. Enfin, nous nous intéressons à l'expérience acquise par les conducteurs novices. Nous étudions le comportement sur la route de l'assuré pour créer de nouvelles classes de risques / In this Ph.D. Dissertation we study the storm guarantee dedicated to the damage caused by the wind and a development of the behavioral insurance through the automobile risk. We associate external information like the wind speed to insurance data. We propose the construction of a storm index to complete and strengthen the evaluation of the damages caused by the major storms. Then we define a partition of the French territory in 6 zones storms, depending on extreme wind correlations to test several scenarios. These various tests and considerations allow us to improve our storm index. We lean on extreme value theory models to show the impact of the variability on the calculation of return periods and capital requirements. We underline the difficulties to obtain strong results in connection with the extreme events. Concerning car insurance, we test various methods to answer the technical and legal evolutions. We characterize the man/woman partition by using the logistic procedure, the multiple correspondence analysis or the classification trees. We show that it is possible to compensate for the absence of the sex variable with other information specific to the insurants or to their vehicle and in particular the use of kilometric data. Finally, we are interested in the acquired experience by young drivers. We study the behavior on the road of the insurants to create new classes of risks